Finite Group Databasebeta

← #29695624

Subgroups — #29695624

Order 15616.

1910 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448769C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446623C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19D4×C22⋊D61—24no—
20D4×C22⋊D61C418yescomplemented
21C2×#14519773C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic, complemented
30#16839838—24no—
31C2×#14519706C2211yescharacteristic, complemented
32#16839765—24no—
33C2×#14519699C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519689C2211yescharacteristic, complemented
43C2×C8×Dic61C2211yescharacteristic, complemented
44#16839662—21no—
45#16839653—21no—
46#16839650—21no—
47#16839631C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic, complemented
49#16839619C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×#11758196—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic, complemented
58C2×#117×C61C2211yescharacteristic, complemented
59C61×#418—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C2×#102×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—28no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—44no—
73C22×C22⋊D61—44no—
74C22×C22⋊D61D411yescharacteristic
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yes—
81C23×Dic61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×#11758189—22no—
84C2×#11758189—22no—
85C2×#11758189—41no—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519773—22no—
89#14519773C2×C414yes—
90#14519751—22no—
91#14519751C2×C414yes—
92#14519749—28no—
93#14519748—22no—
94#14519748C2×C414yes—
95#14519746—28no—
96#14519745—28no—
97D4×Dic61—22no—
98D4×Dic61C2×C414yes—
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519735—22no—
102#14519735—41no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61D411yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61C2311yescharacteristic
120#14519706—22no—
121#14519699—22no—
122#14519699—41no—
123#14519698—22no—
124#14519698—22no—
125#14519698—41no—
126#14519698—41no—
127#14519697—22no—
128#14519697—41no—
129C22⋊#92418—22no—
130#14519689—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C25×C61—21no—
136C22×D4×C61—22no—
137C22×D4×C61—22no—
138C22×D4×C61—21no—
139C22×D4×C61—22no—
140C22×D4×C61—41no—
141C22×D4×C61—41no—
142C22×D4×C61C2×C414yes—
143C22×D4×C61C2311yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×M16×C61—22no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#117×C61—22no—
152#117×C61—41no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C42×C61—21no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160#102×C61D414yescomplemented
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—24no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—81no—
169C24×C61—81no—
170C24×C61C2×D411yescharacteristic
171C23×D61—21no—
172C23×D61—24no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61C2×D411yescharacteristic
180C2×D4×C61—28no—
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—44no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61C22×C412yes—
196C2×D4×C61C22×C412yes—
197C2×D4×C61C2×D412yes—
198C2×D4×C61#4112yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61C22×C412yes—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—22no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—432no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—81no—
226C2×C22⋊D61—81no—
227C2×C22⋊D61C22⋊C414yes—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—42no—
233C22×Dic61—42no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237D4×D61—28no—
238D4×D61—44no—
239D4×D61—44no—
240D4×D61—44no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244C22×C412yes—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61C22×C412yes—
252C2×C4×D61C2×D412yes—
253M16×C61—44no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61C2×D412yescomplemented
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2×D412yescomplemented
264C22⋊C4×C61—42no—
265C42×C61—42no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—81no—
269C22⋊Dic61C22⋊C414yes—
270#11758198—24no—
271#11758198—42no—
272#11758198—81no—
273#11758198C22⋊C414yes—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61C22×C412yes—
280#11758196—42no—
281#11758196—81no—
282#11758196C22⋊C414yes—
283C4×Dic61—42no—
284C4×Dic61—42no—
285C4×Dic61C22×C412yes—
286C4×Dic61C2×D412yes—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293#11758189—44no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—48no—
305C23×C61—48no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—84no—
317C23×C61—84no—
318C23×C61—84no—
319C23×C61—84no—
320C23×C61—84no—
321C23×C61C2×C22⋊C412yes—
322C23×C61C22×D411yescharacteristic
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—22no—
330C22×D61—48no—
331C22×D61—48no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61C2×C22⋊C412yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—48no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61C4×D414yes—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61C2×C22⋊C412yes—
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C22⋊D61—28no—
373C22⋊D61—48no—
374C22⋊D61—48no—
375C22⋊D61—48no—
376C22⋊D61—48no—
377C22⋊D61—84no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—22no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—48no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61C2×C22⋊C412yes—
393C2×Dic61C2×C22⋊C412yes—
394C2×Dic61C2×C22⋊C412yes—
395C2×Dic61AGL(1,ℤ/8)12yes—
396C2×Dic61AGL(1,ℤ/8)12yes—
397D244—22no—
398D244—22no—
399D244—41no—
400D244—41no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C8×C61—22no—
406C8×C61—41no—
407#92418—41no—
408#92418—41no—
409#22428—611nomaximal, Sylow
410C22×C61—24no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—41no—
422C22×C61—42no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—816no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61C22×C22⋊C411yescharacteristic
433C22×C61D4211yescharacteristic
434C22×C61#54611yescharacteristic
435C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
436C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C61#57611yescharacteristic
438C22×C61#57711yescharacteristic
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C4×C61—22no—
455C4×C61—42no—
456C4×C61—81no—
457C4×C61C2×C4×D411yescharacteristic
458C4×C61#51811yescharacteristic
459C4×C61D4211yescharacteristic
460C4×C61#54611yescharacteristic
461Dic61—22no—
462Dic61—22no—
463Dic61—42no—
464Dic61—81no—
465Dic61—81no—
466Dic61#41814yescomplemented
467C2×D42—611no—
468C2×#436—611no—
469C2×#418—611no—
470C2×#418D6111yescharacteristic, complemented
471#2354—611no—
472#1982—611no—
473#1957—611no—
474#1895—611no—
475#1895—611no—
476#1875—611no—
477#1875—611no—
478#1802—611no—
479#1786—611no—
480#1786—611no—
481C4×#102—611no—
482C2×C61—44no—
483C2×C61—42no—
484C2×C61—82no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#327211yescharacteristic
489C2×C61#327411yescharacteristic
490C2×C61#332411yescharacteristic
491C2×C61#332511yescharacteristic
492D61—42no—
493D61—82no—
494C23×D4—611no—
495C23×D4—1221no—
496C23×D4C2×D6111yescharacteristic
497C22×M16—611no—
498C22×M16C2×D6111yescharacteristic, complemented
499D42—618no—
500D42—1224no—
501C2×#127—611no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121—1221no—
505C2×#120—1221no—
506C2×#120—1221no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×#117—611no—
510C2×#117C2×D6111yescharacteristic, complemented
511#436—1224no—
512C2×C4⋊C8—611no—
513#418—24no—
514#418—1224no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102C2×D6111yescharacteristic
524C2×#102C2×D6111yescharacteristic
525C2×#102C2×D6111yescharacteristic, complemented
526C2×#102C2×D6111yescharacteristic, complemented
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C4×C8—611no—
530#390—1221no—
531#388—1221no—
532#388—1221no—
533#384—611no—
534#380—611no—
535#380—611no—
536C4×C4⋊C4—611no—
537C4×C4⋊C4—1221no—
538#340—611no—
539#340—611no—
540#340—611no—
541#340—611no—
542C61#2242811yescharacteristic, complemented, Sylow
543C25—21no—
544C25—1221no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4—611no—
552C22×D4—614no—
553C22×D4—611no—
554C22×D4—1222no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4—1221no—
558C22×D4—1228no—
559C22×D4—1222no—
560C22×D4—1222no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—2441no—
564C22×D4—2441no—
565C22×D4—2444no—
566C22×D4—2444no—
567C22×D4C4×D6114yes—
568C22×D4C22×D6111yescharacteristic
569C22×D4C22×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—1221no—
572C23×C4C22×D6111yescharacteristic
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C2×M16—1222no—
577C2×M16—1222no—
578C2×M16—2441no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6111yescharacteristic
583#127—614no—
584#127—1222no—
585#121—614no—
586#121—614no—
587#121—1228no—
588#121—1222no—
589#121—1222no—
590#120—1228no—
591#120—1228no—
592C4×D4—614no—
593C4×D4—614no—
594C4×D4—614no—
595C4×D4—1222no—
596#117—22no—
597#117—41no—
598#117—1222no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—21no—
618C2×C42—611no—
619C2×C42—1221no—
620C2×C42—1221no—
621C4⋊C8—1222no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—2441no—
630#102—2441no—
631#102—2441no—
632#102—2441no—
633#102C22⋊D6114yescomplemented
634C22⋊C8—1222no—
635C22⋊C8—1222no—
636C4×C8—1222no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640C24—21no—
641C24—21no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24—611no—
650C24—1224no—
651C24—1221no—
652C24—4881no—
653C24—4881no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24D4×D6111yescharacteristic
659C2×D4—28no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—24no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—614no—
675C2×D4—612no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—1228no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—4881no—
690C2×D4—4881no—
691C2×D4—2442no—
692C2×D4—2442no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—24432no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4C2×C4×D6112yes—
704C2×D4C2×C4×D6112yes—
705C2×D4#1175822212yes—
706C2×D4C2×C22⋊D6112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—2442no—
727C22×C4—2442no—
728C22×C4C2×C4×D6112yes—
729C22×C4D4×D6112yes—
730C22×C4D4×D6111yescharacteristic
731C22×C4C23×D6111yescharacteristic
732M16—44no—
733M16—2444no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8C2×C22⋊D6112yescomplemented
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—614no—
750C4⋊C4—612no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—4881no—
757C4⋊C4—2442no—
758C4⋊C4C2×C22⋊D6112yescomplemented
759C22⋊C4—42no—
760C22⋊C4—614no—
761C22⋊C4—614no—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C22⋊C4—1224no—
765C22⋊C4—4881no—
766C22⋊C4—4881no—
767C22⋊C4—2442no—
768C42—42no—
769C42—612no—
770C42—612no—
771C42—2442no—
772C42—2442no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—48no—
784C23—48no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—612no—
801C23—1221no—
802C23—1221no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—1221no—
807C23—1222no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—2448no—
814C23—2448no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23C22⋊C4×D6112yes—
822C23C2×D4×D6111yescharacteristic
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—1228no—
832D4—1222no—
833D4—1222no—
834D4—4884no—
835D4—2448no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2441no—
840D4—2441no—
841D4C4×C22⋊D6114yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—612no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—2448no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4C22⋊C4×D6112yes—
878C2×C4C22×C4×D6111yescharacteristic
879C2×C4C2×D4×D6111yescharacteristic
880C2×C4C22×C22⋊D6111yescharacteristic
881C2×C4C2×#1175822211yescharacteristic
882C2×C4#1451982211yescharacteristic
883C2×C4#1451982211yescharacteristic
884C8—22no—
885C8—41no—
886C8—2441no—
887C8—2441no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—22no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—816no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—48816no—
914C22—4881no—
915C22—4881no—
916C22—4881no—
917C22—4881no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22C2×C22⋊C4×D6111yescharacteristic
926C22D4×C22⋊D6111yescharacteristic
927C22#1684040211yescharacteristic
928C22AGL(1,ℤ/8)×D6111yescharacteristic
929C22AGL(1,ℤ/8)×D6111yescharacteristic
930C22#1684056611yescharacteristic
931C22#1684057211yescharacteristic
932C4—22no—
933C4—42no—
934C4—81no—
935C4—614no—
936C4—1222no—
937C4—1222no—
938C4—4881no—
939C4—4881no—
940C4—2442no—
941C4C2×C4×C22⋊D6111yescharacteristic
942C4#1684023511yescharacteristic
943C4D4×C22⋊D6111yescharacteristic
944C4#1684040211yescharacteristic
945C2—42no—
946C2—44no—
947C2—82no—
948C2—4882no—
949C2—2442no—
950C2C22⋊C4×C22⋊D6111yescharacteristic
951C2#418×D6111yescharacteristic
952C2#2145434411yescharacteristic
953C2#2145741311yescharacteristic
954C2#2145743311yescharacteristic
955C2#2145804611yescharacteristic
956C2#2145805711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22428
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839838C2semidirect
3. C2×#16839765C2semidirect
4. #21448769C2semidirect
5. #21446744C2semidirect
6. #21446623C2semidirect
7. #21446257C2semidirect
8. #21446254C2semidirect
9. #21446141C2semidirect
10. #21446138C2semidirect
11. #21445817C2semidirect
12. #21445750C2semidirect
13. #21445748C2semidirect
14. #102×Dic61C2semidirect
15. C2×C61×#418C2semidirect
18. C22×#11758189C22semidirect
20. D4×C22⋊D61C4semidirect
29. C2×#14519735C22semidirect
31. C2×#14519706C22semidirect
33. C2×#14519699C22semidirect
34. C2×#14519699C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519697C22semidirect
40. C2×#14519697C22semidirect
41. C2×C22⋊#92418C22semidirect
42. C2×#14519689C22semidirect
43. C2×C8×Dic61C22semidirect
47. #16839631C22semidirect
48. #16839622C22semidirect
49. #16839619C22semidirect
50. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C22×M16×C61C22semidirect
58. C2×#117×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×#102×C61C22semidirect
160. #102×C61D4semidirect
259. C2×C8×C61C2×D4semidirect
263. C4⋊C4×C61C2×D4semidirect
466. Dic61#418semidirect
470. C2×#418D61semidirect
498. C22×M16C2×D61semidirect
510. C2×#117C2×D61semidirect
525. C2×#102C2×D61semidirect
526. C2×#102C2×D61semidirect
542. C61#22428semidirect
633. #102C22⋊D61semidirect
745. C2×C8C2×C22⋊D61semidirect
758. C4⋊C4C2×C22⋊D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D4×C22⋊D612
C2×#168398382
C2×#168397652
#214487692
#214467442
#214466232
#214462572
#214462542
#214461412
#214461382
#214458172
#214457502
#214457482
#102×Dic612
C2×C61×#4182
#2242861